+ The sample space is every value of the die (1-6) paired with heads and paired with tails. That is, ${1,2,3,4,5,6} times {H,T}$, with cardinality 12.
+ There are $12^10$ outcomes.
+ If no participants roll a 5, then we omit any outcome in our sample space where the die outcome is 5, leaving us with 10 outcomes of the die and coin. Now we have $10^10$ outcomes. If at least 1 person rolls a 5, then we note that this is simply the complement of the previous result. So we have $12^10 - 10^10$ outcomes total.
]
+ #[
#set enum(numbering: "a)", spacing: 2em)
+ #[
The sample space can be represented as a 6-tuple where the position 1-6
represents balls numbered 1-6, and the value represents the square it
was sent to. So it's
$ {{x_1,x_2,x_3,x_4,x_5,x_6} : x_i in {1,2,3,4}}, i = 1,...6 $
]
+ #[
When the balls are indistinguishable, we can instead represent it as
4-tuples where the position represents the 1st, 2nd, 3rd, or 4th square,
and the value represents how many balls landed. Additionally the sum of all
